Elastic-pulse propagation in thin hollow cones

Elastic pulses were generated in a thin (3-mm) right circular conical shell with apex angle of 20 deg, by an axial impact of a drop weight. Radial-strain pulses of about 250-μs duration were measured at three locations along the cone by semiconductor strain gages. The relative amplitude decrease of the strain pulse was determined as a function of the distance traveled. An approximate analytical solution for this problem is presented. It is shown that, for cones made of material with Poisson's ratio ν=1/3, the approximation leads to the one-dimensional spherical-wave equation and the wave velocity is that of longitudinal waves in thin plates. The decay of amplitude predicted by the model depends on the distance traveled and on the wavelength and it agrees fairly well with the experimental results. The model also gives an upper bound on the amplitude decrease of the pulse.